Phase gratings with odd symmetry for high-resolution lensless optical sensing

ABSTRACT

Image-sensing devices include odd-symmetry gratings that cast interference patterns over a photodetector array. Grating features offer considerable insensitivity to the wavelength of incident light, and to the manufactured distance between the grating and the photodetector array. Photographs and other image information can be extracted from interference patterns captured by the photodetector array. Images can be captured without a lens, and cameras can be made smaller than those that are reliant on lenses and ray-optical focusing.

BACKGROUND

A planar Fourier capture array (PFCA) is an image-sensing device thatemploys an array of angle-sensitive pixels to obviate the needs for amirror, lens, focal length, or moving parts. The pixel array can be madeusing standard integrated-circuit fabrication processes. As aconsequence of these advantages, PFCAs can be made much smaller and lessexpensive than the smallest focusing camera.

Some PFCAs use a near-filed diffraction effect known as the “Talboteffect” to create the angle-sensitive pixels. Such image sensors includetwo diffraction gratings patterned over and in parallel with an array ofphotosensors. The spacing between the gratings is important, and can bedifficult to obtain reliably using inexpensive and readily availablefabrication processes. Moreover, the gratings are sensitive to thewavelength of incident light in a wavelength band of interest, making itdifficult to accurately reproduce color images.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B are cut-away views of a sensing device 100 with anodd-symmetry grating 105 overlying a photodetector array 110 andsimulating light of respective incident planes 115 and 160.

FIG. 2 depicts a binary odd-symmetry grating 200 in accordance with oneembodiment.

FIG. 3 depicts a sensing device 300 in accordance with an embodiment inwhich a binary, odd-symmetry phase grating 305 is formed by an interfacebetween materials of two different refractive indices.

FIG. 4A is a plan view of a sensor 400 in accordance with anotherembodiment.

FIG. 4B is a three-dimensional perspective of sensor 400 of FIG. 4A.

FIGS. 5A, 5B, 5C, and 5D each depict three boundaries of odd symmetry500 over a two-dimensional photodiode array 505.

FIG. 6 depicts three odd-symmetry gratings 600, 620, and 630, each withfeature segments of different relative widths.

FIG. 7A is a cross-section of a phase grating 700 in accordance with anembodiment that uses more than two levels to produce an odd symmetry.

FIG. 7B is a cross-section of a phase grating 710 that is opticallysimilar to phase grating 700 of FIG. 7A but uses fewer layers.

FIG. 8 is a cross-section of a phase grating 800 that illustrates howodd symmetry can be extended to curved functions.

FIG. 9 is a plan view of a grating 900 in accordance with an embodimentin which boundaries of odd symmetry 905 extend radially from the centerof the grating, and in which the widths of the feature segments widengradually away from the center.

FIG. 10 is a plan view of a grating 1000 in accordance with anembodiment with concentric boundaries of odd symmetry 1005, and includesa cut-away view along line A-A.

FIG. 11 is a plan view of a grating 1100 in accordance with anembodiment similar to grating 900 of FIG. 9.

FIG. 12 is a plan view of a grating 1200 in accordance with anotherembodiment.

FIG. 13 depicts a grating 1300 in accordance with another embodiment.

FIG. 14 depicts a grating 1400 and associated photodiode array 1405.

FIG. 15 depicts a grating 1500 and associated photodiode array 1505.

FIG. 16 is a plan view of a grating 1600 in accordance with anembodiment with pentagonal boundaries of odd symmetry 1605.

FIGS. 17A and 17B are plan views of a grating 1700 with boundaries 1705in accordance with another embodiment.

FIG. 18 depicts a two-dimensional array 1800 of gratings 1805 disposedover a photodiode array (not shown).

FIG. 19 is a flowchart 1900 detailing how an image 1905 is captured andresolved in accordance with grating 1700 of FIG. 17.

FIG. 20 depicts lithographic process for forming an image sensor 2000 inaccordance with one embodiment.

The figures are illustrations by way of example, and not by way oflimitation. Like reference numerals in the figures refer to similarelements.

DETAILED DESCRIPTION

FIG. 1A is a cut-away view of a sensing device 100 with an odd-symmetrygrating 105 overlying a photodetector array 110. The features of grating105 offer considerable insensitivity to the wavelength of incident lightin a wavelength band of interest, and also to the manufactured distancebetween grating 105 and photodetector array 110. Grating 105 produces aninterference pattern for capture by array 110. Photographs and otherimage information can then be extracted from the pattern. Images canthus be captured without a lens, and cameras can be made smaller thanthose that are reliant on lenses and ray-optical focusing.

Light in a wavelength band of interest—such as the visible spectrum—isincident grating 105 from a direction 115 that is normal to a transverseplane 120 of the grating 105. Dashed lines 125 highlight periodicboundaries of substantially odd symmetry Each of these boundaries is aresult of features 130 and 135 of odd symmetry, and produces a normallyarranged curtain 140 of minimum intensity created by destructive phaseinterference between adjacent features 130 and 135. Curtains 140 areseparated by foci 145, and the collection of curtains 140 and foci 145(curtains of maximum light intensity) extend from grating 105 throughthe body 150 of device 100 to produce an interference pattern onphotodetector array 110. One photosensitive element 155 within array 110is shaded beneath a focus 145 to serve as a reference for a subsequentdiscussion of the sensitivity of device 100 to the angle of incidentlight.

The image of FIG. 1A resulted from a simulation of a sensing device withthe following parameters and assuming specific parameters. Body 150 isof fused silica, and is in contact with a conventional photodetectorarray 110 with photosensitive elements spaced by 2.2 um. The top ofgrating 105 is an air interface in this example. The relatively smallsegments of features 130 and 135 are about 1 um, and the relativelylarger segments are about 4 um. These segments generally form transverseplane 120, which is separate from array 110 by about 25 um. Curtains 140and foci 145 are the destructive and constructive interference patternsfor 532 nm incident light.

The thickness of body 150 was optimized for 400 nm light despite theselection of 532 nm light for the simulation. As a consequence, thetightest focus occurs about 5 um above array 110 (at the 20 um mark).The resultant curtains 140 plainly separate foci 145 well above andbelow the 20 um mark, however, illustrating a robust insensitivity towavelength within the band of interest. The relatively deep andcontinuous penetration of curtains 140 also provides considerablemanufacturing tolerance for the thickness of body 150.

FIG. 1B depicts sensor 100 of FIG. 1A simulating light incident plane120 at an acute angle 160 to illustrate the sensitivity of curtains 140and foci 145 to the angle of incidence. Using element 155 as a referencepoint, we see that that the foci 145 that shined on element 155 in FIG.1A has considerably moved to the right in FIG. 1B. Curtains 140 and foci145 extend at an acute angle that relates to angle 160 according toSnell's law. The separation of foci 145 by curtains 140 is maintained.Sensor 100 is thus sensitive to the angle of incidence.

FIG. 2 depicts a binary odd-symmetry grating 200 in accordance with oneembodiment. Each of three boundaries of odd symmetry is indicated usinga vertical, dashed line. The upper features of grating 200 are at aheight sufficient to induce one half wavelength of retardation in theband of interest relative to lower features, or π radians of relativephase delay. Features 205 and 210 on either side of each boundaryexhibit odd symmetry with three differently sized segments W₀, W₁, andW₂. With this arrangement, paired segments (e.g., W₀ within features 205and 210) induce respective phase delays that differ by approximatelyhalf a wavelength over the wavelength band of interest.

FIG. 3 depicts a sensing device 300 in accordance with an embodiment inwhich a binary, odd-symmetry phase grating 305 is formed by an interfacebetween materials of two different refractive indices, a polycarbonatelayer 315 and optical lanthanum dense flint glass 320 in this example.Each of four boundaries of odd symmetry 325 is indicated using avertical, dashed line. As in the foregoing examples, the upper featuresof grating 310 induce phase retardations of half of one wavelength (πradians) relative to lower features. Features 330 and 335 on either sideof each boundary exhibit odd symmetry. With this arrangement, pairedfeatures induce respective phase delays that differ by approximatelyhalf a wavelength over the wavelength band of interest.

These elements produce an interference pattern on an analyzer layer 325(e.g., a conventional photodiode array) in the manner detailed inconnection with FIGS. 1A and 1B. This example assumes light incident thelight interface of grating 300 is normal to the transverse plane ofphase grating 310, in which case light beams that enter grating 310equidistant from a one of the boundaries of odd symmetry 325, such as atlocations (−X,0) and (X,0), are out of phase at points beneath array 310(e.g., point (0,Z)), and thus destructively interfere to producecurtains of minimum intensity (e.g., curtains 140 of FIG. 1). Neitherthe depth Z nor the wavelength of light substantially influences thisdestructive interference. Constructive interference similarly producesfoci of maximum intensity (e.g., foci 145 of FIG. 1). Both the high andlow features admit light, which provides relatively high quantumefficiency relative to gratings that selectively block light.

FIG. 4A is a plan view of a sensor 400 in accordance with anotherembodiment. Relatively high segments 405 and low segments 410 on eitherside of each of eight boundaries of odd symmetry 415 create a grating inwhich the widths of the segments increase with distance from the centerof the sensor. For a given focal depth, light of higher frequenciestends to produce a sharper focus with narrower feature widths. Sensor400 can therefore be optimized such that the central portion of thegrating is optimized for collection of relatively higher frequencylight, and the peripheral area for collection of relatively lowerfrequency light. This topic is detailed below in connection with otherFigures.

FIG. 4B is a three-dimensional perspective of sensor 400 of FIG. 4A, andshows how light 420 from a direction normal to the grating surface castsan interference pattern 425 on an underlying photodiode array 430.Curtains and foci, as detailed previously, respectively cast shadows 435and bright shapes 440 to be sensed by individual photosensitive elements445 of array 430. Array 430 captures a digital representation of pattern425.

FIGS. 5A, 5B, 5C, and 5D each depict three boundaries of odd symmetry500 over a two-dimensional photodiode array 505. Curtains 510 castshadows 515 on the underlying photodetectors 520, and the patterns thuscreated are different depending upon the angle of incident light. Array505 can therefore sample the resultant interference pattern to obtaininformation as to the angle of incidence.

FIG. 6 depicts three odd-symmetry gratings 600, 620, and 630, each withfeature segments of different relative widths. It can be useful tocreate a sensor with multiple width ratios, as shown, to compensate formanufacturing tolerances that impact the relative heights of the gratingfeatures. Assuming, for example, that grating 600 is width optimized fora manufacturing process of interest, but that the process produces arelative phase delay of 40% rather than the ideal 50% to form curtainsof minimum intensity at the desired positions. To a first order theincreased width of the relatively wide segments, as depicted in grating630, can improve the distortion resulting from the erroneous phaseoffset. Phase offsets above 50% can be corrected for by narrowing therelatively wide segments, as depicted in grating 620. Some embodimentsinclude a mixture of relative segment widths covering different areas ofa photodiode array to accommodate manufacturing tolerances. Imagesassociated with the gratings that provide the sharpest focus, or thesharpest focus for a wavelength of range of wavelengths, can be selectedor combined to obtain the desired image data. The different gratings mayalso perform better for light of different wavelengths or incidentangles, so selection of which gratings to use for a given image may beoptimized for variables other than manufacturing tolerances.

FIG. 7A is a cross-section of a phase grating 700 in accordance with anembodiment that uses more than two levels to produce an odd symmetry.Additional levels may allow for sharper focus, but may require morecomplex manufacturing processes. If gratings are to be made usingphotolithography, for example, additional levels require additional masksteps. Paired surfaces on either side of each boundary of odd symmetryintroduce respective paired phase delays that differ by approximatelyhalf a wavelength, plus an integer number of wavelengths, over thewavelength band of interest.

FIG. 7B is a cross-section of a phase grating 710 that is opticallysimilar to phase grating 700 of FIG. 7A, but uses fewer layers. Theresultant larger abrupt discontinuities 715 may introduce undesirableimage artifacts or may be difficult to manufacture accurately, but thereduced number of levels may reduce manufacturing costs.

FIG. 8 is a cross-section of a phase grating 800 that illustrates howodd symmetry can be extended to curved functions.

FIG. 9 is a plan view of a grating 900 in accordance with an embodimentin which boundaries of odd symmetry 905 extend radially from the centerof the grating, and in which the widths of the feature segments widengradually away from the center. Grating 900 captures image informationat sixteen discreet angles with a continuously various set of widths.While convenient to draw grating 900 as a circle, other shapes may beused. In some embodiment, for example, collections of gratings arearrayed over a photodiode array. In such cases grids that share commonboundaries (e.g., such as hexagonal, square, or triangular boundaries)make more efficient use of the underlying photodiodes.

FIG. 10 is a plan view of a grating 1000 in accordance with anembodiment with concentric boundaries of odd symmetry 1005, and includesa cut-away view along line A-A. In this example the widths of thefeature segments are discrete and the angles are continuous. The spacingof grating 1000 appear consistent, but may be varied to allow for sharpfocus for a range of wavelengths, angles of incidence, or manufacturingvariations.

FIG. 11 is a plan view of a grating 1100 in accordance with anembodiment similar to grating 900 of FIG. 9. The two halves of grating900 provide essentially the same information. Grating 1100 addshalf-circle polarization filters 1105 and 1110 with perpendicularorientations. Each half of grating 1100 thus produces image dataspecific to one of two polarizations, and these data can be usedseparately or together. More or fewer filters, with the same ordifferent orientations, may be used in other embodiments. Differenttypes of filters can also be used to cover all or a portion of gratingsof the type described herein.

FIG. 12 is a plan view of a grating 1200 in accordance with anotherembodiment. Curved boundaries of odd symmetry 1205 extend radially fromthe center of the grating, and the widths of the feature segments widengradually away from the center. The curvature of boundaries 1205 providecontinuously varying angular information similar to what is availablefrom grating 1000 of FIG. 10 while retaining the continuously varyingspacings of grating 900 of FIG. 9.

FIG. 13 depicts a grating 1300 in accordance with another embodiment. Asnoted previously, different widths of the grating features providesharper focus for different colors of light within the wavelength bandof interest. Grating 1300 has the same radial symmetry of grating 900 ofFIG. 9, but those areas for which the spacing is optimized for blue,green, and red light are provided with filters to admit their respectivewavelengths. Omitting wavelengths that provide a blurred interferencepattern on the underlying analyzer can improve image sharpness. Grating1300 is bounded by an opaque mask 1305 that defines the limit of theaperture.

FIG. 14 depicts a grating 1400 and associated photodiode array 1405.Grating 1400 has parallel odd-symmetry boundaries 1410, which may havefeatures of the same or different widths, or of varying widths along oneor more boundaries. Parallel boundaries with the requisite diversity ofwidths and spacings to sample a sufficient number of spatial frequenciescan image e.g. barcodes. Array 1405 is shown alongside, rather thanbelow, grating 1400 to highlight the angle θ_(A) between the directionof boundaries 1410 and the columns of photosensitive elements in array1405. Angle θ_(A) creates more diversity of measurements because thelinear shadow covers different percentages of pixels in different rows.In one embodiment angle θ_(A) is selected so that the top of eachboundary is offset from the bottom by about one pixel of array 1405.

FIG. 15 depicts a grating 1500 and associated photodiode array 1505.Grating 1500 has parallel, right-angled boundaries 1510, which may havefeatures of the same or different widths, or of varying widths along oneor more boundaries. Parallel boundaries with the requisite diversity ofwidths and spacings along two dimensions to sample a sufficient numberof spatial frequencies can image e.g. point sources, such as to identifythe position of the sun. Angle θ_(A) can be introduced for the reasonspresented above in connection with FIG. 14.

FIG. 16 is a plan view of a grating 1600 in accordance with anembodiment with pentagonal boundaries of odd symmetry 1605. In thisexample the widths of the feature segments are discrete, but they canvary along one or more boundaries in other embodiments. Straightboundaries may be advantageous over curved ones because line segmentscan more easily provide precise odd symmetry.

Grating 1600 provides information at five different orientations. Otherboundary shapes, such as other polygons, are used in other embodiments.In general, polygons with odd numbers of sides provide greaterorientation diversity than polygons with a similar but even number ofsides (e.g., a pentagon provides more orientation diversity than asquare or a hexagon).

FIG. 17A is a plan view of a grating 1700 in accordance with anotherembodiment. Recalling that relatively narrow (wide) segment spacingworks better for relatively high (low) frequencies, feature spacingincreases along odd-symmetry boundaries (between dark and light regions)with distance from the center. Curved boundaries of odd symmetry 1705extend radially from the center of the grating to the periphery,radiating out between the dark (elevated) and light (recessed) arms nearthe center. The curved boundaries are obscured by grating features inFIG. 17A, so the shapes of boundaries 1705 are depicted in FIG. 17B forease of review.

The segment widths do not continue to increase with radius, as there isa maximum desired width for a given wavelength band of interest (e.g.,the widest may correspond to the lowest frequency of visible red light).The features that define boundaries 1705 therefore exhibitdiscontinuities as they extend toward the periphery of grating 1700. Inthis example, grating 1700 has three discrete areas each tuned to asubset or all of the wavelengths in the band of interest.

FIG. 18 depicts a two-dimensional array 1800 of gratings 1805 disposedover a photodiode array (not shown). Each of gratings 1805 is identical,but any number of parameters, many of which are discussed previously,can be varied within and among gratings 1805. For example, differentshapes and types of gratings can be used to create and image differenttypes of interference patterns that can be combined or used separatelyto obtain some desired result. The decision to consider all or aspecific subset of information generated by one or more of theconstituent gratings can be done once, such as at time of manufacture toaccommodate process variations, or can be done dynamically to highlightdifferent aspects of a scene. Emphasizing aspects of different patternscan be used, for example, to highlight light of different polarities,wavelengths, or angles of incidence.

Spaced gratings facing the same direction, particularly when theircharacteristics are well matched, can be used to sense moving objects.Assuming matched gratings with a fixed separation receiving light fromthe same scene, the difference between the photocurrents of therespective analyzer layers is sensitive only to objects relatively closeto the pair. Further, the time derivative of this difference issensitive to nearby, moving objects, and is insensitive to relativelydistant moving or stationary objects.

FIG. 19 is a flowchart 1900 detailing how an image 1905 is captured andresolved in accordance with grating 1700 of FIG. 17. First, an image1910 is presented such that light from image 1910 is incident grating1700. The incident light passes through phase grating 1700 to produce anintensity pattern 1920 on an underlying two-dimensional array ofphotosensors (not shown), which captures the pattern (1915). Thecaptured pattern 1920 may appear unintelligible to a human; however,because grating 1700 has sharp features in its point-spread function(PSF), the pattern contains rich information about the image.

The PSF of grating 1700, possibly in combination with the underlyingarray, is known from a prior calibration or high-fidelity simulation.The way in which the PSF varies as a function of incident angle andcolor may also be similarly determined. This information is representedby a response 1930. A mathematical conversion based on this response canthus be used to reconstruct image 1910 from pattern 1920.

To recover the original image, responses 1920 and 1930 are combined toform an inverse problem (1925), which is solved (1935) to recover aversion 1940 of the original image. One embodiment employs thewell-known Tikhonov regularized inversion technique to accomplish steps1925 and 1935. Take as a starting point a) detailed knowledge of the PSFof grating 1700, b) knowledge of the noise level of the system undercurrent illumination conditions, and c) the specific readings observedfor this image (pattern 1915). Express the unknown image as an N×1vector x, where N is the total number of pixels one wishes toreconstruct. Express the readings from the photosensor as an M×1 vectory, where M is the total number of photosensors in the array. Expressdetailed knowledge of the PSF as an M×N matrix A such that for any imagex, the formula expected observed signal y under x is y=Ax, called the“forward equation.”

To reconstruct an image, it suffices to solve the forward equation witha known measurement vector y for an unknown image x as follows. Multiplyboth sides of the forward equation by the transpose of A (A^(T)) toobtain A^(T) y=A^(T) Ax. The matrix A^(T) A is square and in principlecould be directly inverted to recover x; however usually this inversionis poorly conditioned when noise is present and when not alleigenvectors of A^(T) A have equally large associated eigenvalues. Thusin practice, Tikhonov regularization (as follows) usually deliverspreferable results.

Next, select a regularization parameter λ>0 based on the noise level atthe current illumination conditions. Finally, invert the matrix (A^(T)A+λI) (where I is the identity matrix), assume (A^(T) A+λI)≈(A^(T) A)and multiply on the left of the preceding equation to obtain x≈(A^(T)A+λI)⁻¹ A^(T) y. Therefore, for a given regularization parameter λ, theimage recovered through Tikhonov regularization is a linear combinationof the readings from the photosensor. If the PSF is sufficientlyspatially invariant to the extent that its spatial dependence can beneglected, these computations can be done in the Fourier domain,allowing for much faster numerics.

Another embodiment recovers the matrix x using compressed sensing. Ifthe scene is expected to be sparse in some basis (such as a wavelettransform W for natural images), the following methodology can be used.We can recover the sparse scene components z where x=Wz by finding the zthat minimizes the following cost function: ½ r^(T)r+λf(z), where r isthe residual (y−AWz), λ>0 is a regularization parameter (different fromin (5), but also noise-dependent), and f(z) is a function penalizingnon-sparse z. If f(z) is a convex function of z such as the L₁ norm,this optimization problem can be solved efficiently using convexoptimization techniques. The penalty function f(z) can also take onother forms, including terms penalizing total variation in thereconstructed image x or other prior scene knowledge.

Some of the chief advantages of compressed sensing over linearapproaches such as Tikhonov regularization are that the former allowmore prior information about the expected scene structure to help shapethe final image. Further, if A^(T) A does not have full rank or cannotmeasure certain aspects of the scene (for example, due to some near-zeroregions of the 2D Fourier transform of the PSF), using compressedsensing sometimes overcomes these limitations given correct priorinformation about the expected images.

The foregoing Tikhonov and compressed-sensing techniques can includeiterative methods to reduce problem complexity. For example,Richardson-Lucy deconvolution can iteratively approximate Tikhonovregularized inversion and iterated wavelet thresholding can be anumerically efficient way to converge to a compressed-sensing-likesolution.

In some embodiments the purpose of the sensor is not to reconstruct animage, but to perform some optical sensing task. In such cases thevector x may represent the sought measurement rather than the field ofimage pixels, and the forward transform A can be appropriately modified.

FIG. 20 depicts lithographic process for forming an image sensor 2000 inaccordance with one embodiment. First, a wafer 2005 of material that istransparent over the wavelength band of interest is patterned with amask 2010 that defines the relatively high features of what will becomean odd-symmetry grating surface of the type detailed herein. Next, theexposed surface of wafer 2005 is etched to create recessed regions 2015.Mask 2010 is then removed. Finally, wafer 2005, now comprising agrating, is bonded to a photodiode array 2025. Photolithographic andwafer-bonding processes are well known to those of skill in the art, soa detailed discussion is omitted.

While the present invention has been described in connection withspecific embodiments, other embodiments are also envisioned. Forexample, while each grating detailed previously may be used inconnection with photoreceptors to collect incident light, gratings inaccordance with these and other embodiments can be used more generallyin imaging devices that project images from photo-emitters rather thanor in addition to sensing them. Other variations will be evident tothose of skill in the art. Therefore, the spirit and scope of theappended claims should not be limited to the foregoing description. Onlythose claims specifically reciting “means for” or “step for” should beconstrued in the manner required under the sixth paragraph of 35 U.S.C.§ 112.

What is claimed is:
 1. A sensing device comprising: a photodetectorarray; and a phase grating overlying the photodetector array anddefining a transverse plane, the phase grating transparent over awavelength band of interest and producing, for light in the wavelengthband of interest incident the phase grating and normal to the transverseplane of the phase grating, normally arranged curtains of minimumintensity between the phase grating and the photodetector array, each ofthe curtains of minimum intensity created by destructive phaseinterference between a first part of the light passing through a firstphase-grating feature located to one side of the curtain and a secondpart of the light passing through a second phase-grating feature locatedto the other side of the curtain; wherein the first phase-gratingfeatures induce a first phase delay to the first part of the light andthe second phase-grating features induce a second phase delay to thesecond part of the light, the first phase delay different from thesecond phase delay by half of a wavelength, plus an integer number ofthe wavelength, over the wavelength band of interest.
 2. The sensingdevice of claim 1, wherein the phase grating features are locally oddsymmetric about each of the normally arranged curtains of minimumintensity.
 3. The sensing device of claim 1, wherein for light in thewavelength band of interest incident the phase grating at a first anglerelative to the transverse plane of the phase grating the curtainsextend from the phase grating at a second angle, also relative to thetransverse plane, that is a function of the first angle.
 4. The sensingdevice of claim 3, wherein the second angle is independent of wavelengthwithin the wavelength band of interest.
 5. The sensing device of claim4, wherein the second angle is independent of a separation between thephotodetector array and the phase grating.
 6. A sensor comprising: aphotodetector array to detect light over a wavelength band of interest;and a phase grating transparent to the light over the wavelength band ofinterest, overlying the photodetector array, and defining a transverseplane, the phase grating including first phase-grating features toinduce a first phase delay to the light and second phase-gratingfeatures to induce a second phase delay to the light, each of the firstphase-grating features and a corresponding one of the secondphase-grating features forming between them a boundary of odd symmetryextending in the transverse plane, the boundaries of odd symmetrydiverging from one another in the transverse plane; wherein the firstphase delay differs from the second phase delay by half of a wavelength,plus an integer number of the wavelength, over the wavelength band ofinterest.
 7. The sensor of claim 6, wherein the boundaries of oddsymmetry are arranged in a spiral pattern.
 8. The sensor of claim 7,wherein the boundaries of odd symmetry are discontinuous.
 9. The sensorof claim 6, wherein each of the boundaries of odd symmetry extends awayfrom a center, and wherein the first phase-grating features and pairedsecond phase-grating features associated with each of the boundaries ofodd symmetry preferentially focuses blue wavelengths relative to redwavelengths on the photodetector array near the center andpreferentially focuses red wavelengths relative to blue wavelengths onthe photodetector array relatively farther from the center.
 10. Thesensor of claim 6, wherein the paired first and second phase-gratingfeatures are of radial symmetrical from a perspective normal to thetransverse plane.
 11. The sensor of claim 6, wherein the firstphase-grating features include first features of a first dimensionparallel to the transverse plane and second features of a seconddimension greater than the first dimension parallel to the transverseplane.
 12. The sensor of claim 11, wherein the second phase-gratingfeatures include third features of the first dimension parallel to thetransverse plane and fourth features of the second dimension parallel tothe transverse plane.
 13. A method for capturing an image of a scene,the method comprising: modulating light from the scene through a phasegrating to produce an interference pattern, the phase grating includingfirst phase-grating features to induce a first phase delay to the lightfrom the scene and second phase-grating features to induce a secondphase delay to the light from the scene, wherein the first phase delaydiffers from the second phase delay by half of a wavelength, plus aninteger number of the wavelength, over a wavelength band of interest,each pair of one of the first phase-grating features and one of thesecond phase-grating features forming between them a boundary of oddsymmetry extending in a transverse plane, the boundaries of odd symmetrydiverging from one another in the transverse plane; and sampling theinterference pattern.
 14. The method of claim 13, wherein the boundariesof odd symmetry are arranged in a spiral pattern.
 15. The method ofclaim 13, wherein the boundaries of odd symmetry are discontinuous. 16.The method of claim 13, wherein the sampling the interference patterncaptures information as to angles of the light from the scene.
 17. Themethod of claim 16, further comprising inverting the information toestimate a light field representative of the scene.
 18. The method ofclaim 17, further comprising, before the inverting, combining a responseof the phase grating with noise to form an inverse problem, whereininverting the information comprises solving the inverse problem.
 19. Themethod of claim 17, further comprising generating an image of the scenefrom the estimated light field.